Question

the minute hand of a clock is 9 inches long and moves from 12 to 8 oclock. how far does the tip of the minute hand move? express your

the minute hand moves
(simplify your answer. type your answer in terms of $pi$. use integers or fractions for any numbers in the expression.)

the minute hand moves approximately
(round your answer to two decimal places.)

Explanation:

Step1: Determine the fraction of the circle traversed

The minute - hand moves from 12 to 8, which is $\frac{8}{12}=\frac{2}{3}$ of a full - circle.

Step2: Recall the formula for the circumference of a circle

The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius of the circle. Here, the length of the minute - hand is the radius, so $r = 9$ inches.

Step3: Calculate the distance the tip of the minute - hand moves

The distance $d$ the tip of the minute - hand moves is the fraction of the circle times the circumference. So $d=\frac{2}{3}\times2\pi r$. Substitute $r = 9$ into the formula: $d=\frac{2}{3}\times2\pi\times9$.
\[

$$\begin{align*} d&=\frac{2\times2\pi\times9}{3}\\ &= 12\pi \end{align*}$$

\]

Step4: Approximate the value

To approximate the value, substitute $\pi\approx3.14159$. Then $d\approx12\times3.14159 = 37.70$ inches.

Answer:

The minute hand moves $12\pi$ inches.
The minute hand moves approximately $37.70$ inches.